In this section, we discuss the application part of the of supremum cosine angle. In sampling theory, it is desirable for the sampling operator to be one-to-one for the unique representation of a function. We find out the conditions under which the sampling operator defined for a Bessel MG system is one-to-one. We also connect our result with the injectivity of the pointwise sampling operator defined on each fiber space. The results obtained in this section are an abstract version of results already obtained for closed subspaces of a separable Hilbert space or more generally shift invariant spaces [1]}, [2]}.
We begin with some definitions.
